vinayparamanand
Four friends Laura, Nancy, James and Simon buy some pencils, pens and erasers from a shop. Laura buys 5 pencils, 6 pens, and 1 eraser for $17.50. Nancy buts 3 pens, 3 pencils, and 2 erasers for $ 10. James buys 5 pens, 2 pencils, and 5 erasers for $14.50. How much will Simon have to pay if he buys 3 pens, 2 pencils, and 5 erasers?
Note: How often in the GMAT do such questions appear?
Can i have a generic way to solve such questions?
A: $9.5
Let the cost of a pencil be $x
Let the cost of a pen be $y
Let the cost of a erasers be $z
Now,
for Laura 5x+6y+z = 17.50 ----a
for Nancy 3x+3y+2z=10 ----b
for James 2x+5y+5z=14.50 ---c
We have to find value for Simon i.e 3x+2y+5z=??
Now,
2b - a => x + 3z = 2.5 ----d
5b - 3c => 9x - 5z = 6.5 ------e
Solving, d and e
9d - e => 9x + 27z - (9x-5z ) = 22.5 - 6.5
32z = 16
z = 1/2
putting z in d, we get x = 1
putting z and x in a we get y= 2
3x + 2y +5z = 3 + 4 + 2.5 => 9.5$
Thanks,
Jai
KUDOS if it HELPED..!!!